Unfazed by its roots?

Calculus Level pending

Which of the following statements is/are true?

(A): If P(x)P(x) is a quadratic polynomial with real roots, then 1P(x)dx\int \frac1{P(x)} \, dx has a closed form.

(B): If P(x)P(x) is a quadratic polynomial with non-real roots, then 1P(x)dx\int \frac1{P(x)} \, dx has a closed form.

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